# Being Curious

Being Curious is part of our Developing Mathematical Habits of Mind collection.

Good thinkers are curious and ask good questions. They are excited by new ideas and are keen to explore and investigate them.

How do we encourage our students to become more curious mathematicians?

These problems will exploit students' natural curiosity and provoke them to ask good mathematical questions.

You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.

### Being Curious - Number

Number problems for inquiring students.

### Being Curious - Algebra

Algebra problems for inquiring students.

### Being Curious - Geometry

Geometry problems for inquiring students.

### Being Curious - Statistics

Statistics problems for inquiring students.

### Nice or Nasty

##### Age 7 to 14Challenge Level

There are nasty versions of this dice game but we'll start with the nice ones...

### Statement Snap

##### Age 7 to 14Challenge Level

You'll need to know your number properties to win a game of Statement Snap...

### Perimeter Possibilities

##### Age 11 to 14Challenge Level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

### How Much Can We Spend?

##### Age 11 to 14Challenge Level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

### Can They Be Equal?

##### Age 11 to 14Challenge Level

Can you find rectangles where the value of the area is the same as the value of the perimeter?

### Shifting Times Tables

##### Age 11 to 14Challenge Level

Can you find a way to identify times tables after they have been shifted up or down?

### Summing Consecutive Numbers

##### Age 11 to 14Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

### Satisfying Statements

##### Age 11 to 14Challenge Level

Can you find any two-digit numbers that satisfy all of these statements?

### Special Numbers

##### Age 11 to 14Challenge Level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

### Largest Product

##### Age 11 to 14Challenge Level

Which set of numbers that add to 10 have the largest product?

##### Age 11 to 14Challenge Level

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

### Dicey Operations

##### Age 11 to 14Challenge Level

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

### Blue and White

##### Age 11 to 14Challenge Level

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

### Elevenses

##### Age 11 to 14Challenge Level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

### Number Pyramids

##### Age 11 to 14Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### More Number Pyramids

##### Age 11 to 14Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Estimating Time

##### Age 11 to 14Challenge Level

How well can you estimate 10 seconds? Investigate with our timing tool.

### Right Angles

##### Age 11 to 14Challenge Level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

### On the Edge

##### Age 11 to 14Challenge Level

If you move the tiles around, can you make squares with different coloured edges?

### Reversals

##### Age 11 to 14Challenge Level

Where should you start, if you want to finish back where you started?

### Two's Company

##### Age 11 to 14Challenge Level

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

### Sending a Parcel

##### Age 11 to 14Challenge Level

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

### Unequal Averages

##### Age 11 to 14Challenge Level

Play around with sets of five numbers and see what you can discover about different types of average...

### Cosy Corner

##### Age 11 to 14Challenge Level

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

### Non-transitive Dice

##### Age 11 to 14Challenge Level

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

### Think of Two Numbers

##### Age 11 to 14Challenge Level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

### Who's the Best?

##### Age 11 to 14Challenge Level

Which countries have the most naturally athletic populations?

### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

### Square Coordinates

##### Age 11 to 14Challenge Level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

### Opposite Vertices

##### Age 11 to 14Challenge Level

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

### Stars

##### Age 11 to 14Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

### A Chance to Win?

##### Age 11 to 14Challenge Level

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

### Cola Can

##### Age 11 to 14Challenge Level

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

### Which Solids Can We Make?

##### Age 11 to 14Challenge Level

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

### Litov's Mean Value Theorem

##### Age 11 to 14Challenge Level

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

### Arithmagons

##### Age 11 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges?

### What's it Worth?

##### Age 11 to 16Challenge Level

There are lots of different methods to find out what the shapes are worth - how many can you find?

### Charlie's Delightful Machine

##### Age 11 to 16Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Marbles in a Box

##### Age 11 to 16Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### Cuboid Challenge

##### Age 11 to 16Challenge Level

What's the largest volume of box you can make from a square of paper?

### Searching for Mean(ing)

##### Age 11 to 16Challenge Level

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

### Take Three from Five

##### Age 11 to 16Challenge Level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

### Curvy Areas

##### Age 14 to 16Challenge Level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

### How Old Am I?

##### Age 14 to 16Challenge Level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

### A Little Light Thinking

##### Age 14 to 16Challenge Level

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

##### Age 14 to 16Challenge Level

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

### Beelines

##### Age 14 to 16Challenge Level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### Pair Products

##### Age 14 to 16Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

### Last One Standing

##### Age 14 to 16Challenge Level

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

### Trapezium Four

##### Age 14 to 16Challenge Level

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

### Pick's Theorem

##### Age 14 to 16Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

### Arclets

##### Age 14 to 16Challenge Level

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

### Same Number!

##### Age 14 to 16Challenge Level

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

### Triangle Midpoints

##### Age 14 to 16Challenge Level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

### Multiplication Arithmagons

##### Age 14 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

### Partly Painted Cube

##### Age 14 to 16Challenge Level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

### Triangles and Petals

##### Age 14 to 16Challenge Level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

### Where to Land

##### Age 14 to 16Challenge Level

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

### What's Possible?

##### Age 14 to 16Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

### Odds and Evens Made Fair

##### Age 14 to 16Challenge Level

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

### Hexy-metry

##### Age 14 to 16Challenge Level

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

### Mathsland National Lottery

##### Age 14 to 16Challenge Level

Can you work out the probability of winning the Mathsland National Lottery?

### Fit for Photocopying

##### Age 14 to 16Challenge Level

Explore the relationships between different paper sizes.

### Vector Journeys

##### Age 14 to 18Challenge Level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

### Data Matching

##### Age 14 to 18Challenge Level

Use your skill and judgement to match the sets of random data.

### Which Spinners?

##### Age 14 to 18Challenge Level

Can you work out which spinners were used to generate the frequency charts?

### Three by One

##### Age 16 to 18Challenge Level

There are many different methods to solve this geometrical problem - how many can you find?